Was Douglas, from what we hear of his fearless character, a man who would be likely to give up his wedding ring at such short notice, or could we conceive of his giving it up at all?
No, no, Watson, the assassin was alone with the dead man for some time with the lamp lit.

Of that I have no doubt at all.
"But the gunshot was apparently the cause of death.

Therefore the shot must have been fired some time earlier than we are told.

But there could be no mistake about such a matter as that.

We are in the presence, therefore, of a deliberate conspiracy upon the part of the two people who heard the gunshot--of the man Barker and of the woman Douglas.